Give possible expressions for the length and breadth of each of the following rectangles:

(i) Area: 25a² – 35a + 12

Since, area is product of length and breadth therefore by factorizing the given area, we can know the length and breadth of rectangle

25a² – 35a + 12

= 25a² – 15a – 20a + 12

= 5a (5a – 3) – 4 (5a – 3)

= (5a – 4) (5a – 3)

Possible expression for length = 5a – 4

Possible expression for breadth = 5a – 3

(ii) Area: 35y² + 13y – 12

35y² + 13y – 12

= 35y² – 15y + 28y – 12

= 5y (7y – 3) + 4 (7y – 3)

= (5y + 4) (7y – 3)

Possible expression for length = (5y + 4)

Possible expression for breadth = (7y – 3)